Lecture 2-2C: Fundamental Forces: Gravity

Newton's 2nd Law: The velocity of an object is changed through an acceleration, which occurs when a net force acts on an object:

force = vector quantity generator of motion

units of kg m/s2 = Newtons

mass = scalar quantity resistance to change in

motion

Act through contact Support (normal) force

Friction & Viscosity Tension

Spring action Bouyancy Pressure

Types of forces

Act over distance Gravitational force

Electromagnetic force Strong force Weak force

four fundamental forces of nature

Fundamental forces all act at a distance, but on different scales all act on a certain quality of an object

Force Quality acted on Scale Manifestation

Gravity mass planetary to universal Earth orbit around Sun

Electromagnetism charge atomic to planetary

Molecular bonds, magnets

Strong color charge nuclear Elements beyond

hydrogen; fusion

Weak weak isospin nuclear Radioactive decay

Gravity is an attractive force that acts on mass It is only important on macroscopic scales

Gravitational force

image credit: NASA http://nssdc.gsfc.nasa.gov/image/planetary/earth/near_earth_moon.jpg

Local Gravity: the Weight Force

Weight force mass surface gravity

Weight and surface gravity both point toward the center of the Earth; Average surface gravity g = 9.81 m/s2

Weight ≠ mass

Newton ≠ kilogram Pounds ≠ slug

Astronaut on the Moon image; NASA

70 kg astronaut: on Earth: g = 9.81 m/s2

FW = 690 N on Moon: g = 1.62 m/s2

FW = 110 N

Force of Earth acting on you = Force of you acting on Earth

Constant acceleration

Surface gravity gives rise to constant downward acceleration independent of mass

Constant acceleration experiment by Apollo 15 astronauts on the Moon

Original video credit: NASA: https://www.youtube.com/watch?v=5C5_dOEyAfk

Weightlessness The weight force is always present, but in an accelerated frame of reference we can perceive weightlessness

Weightlessness on the International Space Station (NASA TV: https://youtu.be/FdQA-pE2luQ?t=4m45s

Weightlessness on Reduced Gravity Flight

Image Credit: NASA

Universal Gravitational Force Law Newton connected surface gravity near Earth to planetary motion with a single force law

force of gravity from 1 acting on 2

masses of two objects

direction pointing

from 1 to 2

distance between

objects universal gravitational force constant = 6.674x10-11 N m2/kg2

Kepler's Laws of Planetary Motion

1. An orbit is an ellipse with the Sun at one focus

Circular motion => inward radial acceleration required - this is provided by gravitational interaction with Sun

ac = Fg/m vφ

Kepler's Laws of Planetary Motion

2. A planet moves faster when it is closer to the Sun

Force of gravity, and hence acceleration are greater at smaller separations (ac = Fg/m = GMS/r2)

vφ ac = Fg/m

vφ

ac = Fg/m

Kepler's Laws of Planetary Motion

3. The orbit period of a planet (P) and orbit radius (r) scale as P2/r3 = constant

vφ

vφ

Connecting Gravitation with Weight

Connecting Gravitation with Weight

Connecting Gravitation with Weight

Connecting Gravitation with Weight

Connecting Gravitation with Weight

Connecting Gravitation with Weight

Gravity and Electrostatic Forces

Both Gravity and Electrostatic forces have 1/r2 distance dependence

masses charges

gravitational constant

electrostatic constant

Summary Four fundamental forces of nature are gravity,

electromagnetism, strong & weak These are all non-contact forces and act over different

scales and on different qualities Gravity is an attractive force acting on mass Weight is the manifestation of gravitational attraction

with Earth near its surface; it is distinct from mass Weightlessness is perceived in "free fall" situations Newton's Law of Gravity unifies weight and planetary

motion (Kepler's Laws), applies universally